Answered: 7-12. A particle of mass m rests on a… | bartleby

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Theoretical Mechanics Topic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion >Generate equations for (x,y), (Vx,Vy), V², T > L = T-U --- For study purposes. Thank you!

7-12. A particle of mass m rests on a smooth plane. The plane is raised to an inclination
angle at a constant rate a (0 = 0 at t = 0), causing the particle to move down the
plane. Determine the motion of the particle.

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A massless spring with equilibrium length d and spring constant k connects two particles. The system is flat and horizontal, yet it may spin and vibrate (ccompress\stretch).1- Determine the system's Lagrangian.2- Determine the system's Hamiltonian.3- Calculate Hamilton's equations of motion. It should be noted that the generalized momenta can be omitted. -It is worth noting that as the mass spins, it begins to expand. Hint: make your coordinate system's origin the center of the unstretched spring. also In generalized coordinates of (r_i) and (theta_i) , express your equations.
Theoretical Mechanics Topic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion >Generate equations for (x,y), (Vx,Vy), V², T > L = T-U --- For study purposes. Thank you!
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Theoretical Mechanics Topic: Lagrangian and Hamiltonian Dynamics >Generate the necessary equations to this system. > Use the equations of motion >Generate equations for (x,y), (Vx,Vy), V², T > L = T-U --- For study purposes. Thank you!